Since \(p_1+\cdots +p_{m_0}+(g-m_0)\infty _+\)  is a general divisor, \(\theta (\int _{\infty _+}^p {\rm d}{v}+e)\)  has a zero of order \(g-m_0\)  at \(\infty _+\)  by Riemann's theorem [1]}. Therefore
\(\theta _0:=\frac{1}{(g-m_0)!}\left( \left(\sum _{j=1}^g\frac{{\rm d} v_j}{{\rm d} z}\frac{\partial }{\partial z_j}\right)^{g-m_0}\theta \right)(e\,|\,\Omega )\) 
